LAFC claimed derby honours in Los Angeles thanks to second-half goals from Danny Musovski and star Carlos Vela on Monday (AEDT).
The Galaxy – without stuttering former Manchester United and Real Madrid forward Javier Hernandez – was dealt a blow in the 25th minute when centre-back Giancarlo Gonzalez was red carded after denying a goal-scoring opportunity.
Referee Kevin Stott had initially awarded a penalty and shown Gonzalez a yellow card before VAR intervened, with Diego Rossi brought down just outside the box as the Galaxy defender saw red.
LAFC had gone 238 minutes without scoring against the Galaxy – having averaged a goal every 28.6 minutes in the first seven derbies – but that drought ended courtesy of Musovski's 58th-minute opener at Banc of California Stadium, the forward getting on the end of Rossi's throughball.
Vela came off the bench with 20 minutes remaining for his first appearance since August 22 due to a medial collateral ligament (MCL) injury.
The reigning MVP capped his long-awaited comeback for the Supporters' Shield holders with a goal in the third minute of stoppage time, taking Vela to 23 goals from his previous 22 MLS matches at Banc of California Stadium.
With the result, LAFC are fourth in the Western Conference and five points adrift of leaders Sporting Kansas City, while the Galaxy remain rooted to the foot of the table.